All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 5 Lesson 2 Estimate Sums and Differences will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 5 Lesson 2 Estimate Sums and Differences
One way to estimate is to use rounding. If you round numbers to a lesser place value, you are likely to get an estimate that is closer to the exact answer.
Math in My World
Example 1
Hadassah used a digital thermometer to find the morning temperature and afternoon temperature. She found the morning temperature was 31.3°F and the afternoon temperature was 37.6°F. Estimate the difference in average temperatures.
One Way:
Round to the nearest ten.
Round 37.6 to the nearest ten.
37.6 → ___________
Round 31.3 to the nearest ten.
31.3 → ____________
Subtract.
__________ – __________ = ____________
Answer:
Round 37.6 to the nearest ten is 40.
Round 31.3 to the nearest ten is 30.
10
Explanation:
Given,
The morning temperature was 31.3°F
The afternoon temperature was 37.6°F
We have to find Round to the nearest ten.
Round 37.6 to the nearest ten is 40.
We have to round off the digit after the decimal point if the digit is more than 5.
Round 31.3 to the nearest ten is 30.
If the digit is less than 5 then we don’t have to do anything.
Now subtract 40 – 30 = 10
Another Way:
Round to the nearest one.
Round 37.6 to the nearest one.
37.6 → _____________
Round 31.3 to the nearest one.
31.3 → _____________
Subtract.
_________ – ___________ = ____________
The difference is about ___________°F or about ___________°F.
The actual difference is 6.3°F. So, rounding to the nearest ___________ gave the more accurate estimate.
Answer:
Round 37.6 to the nearest one is 38.
Round 31.3 to the nearest one is 31.
38 – 31 = 7
The difference is about 10°F or about 7°F.
The actual difference is 6.3°F. So, rounding to the nearest one gave the more accurate estimate.
Explanation:
Given,
The morning temperature was 31.3°F
The afternoon temperature was 37.6°F
Now we need to round to the nearest one.
31.3°F = 31
37.6°F = 38
The difference is 38 – 31 = 7
The difference is about 10°F or about 7°F and the actual difference is 6.3°F.
So, rounding to the nearest one gave the more accurate estimate.
Example 2
Estimate 5.26 + 1.93 by rounding to the nearest one.
5.26 → _____________
1.93 → _____________
Helpful Hint
You will learn how to find the actual sum in a later lesson. The actual sum is 7.19, so 7 is a fairly accurate estimate.
Add.
____________ + ____________ = ___________
The sum is about _____________.
Answer:
The answer is 7.
Explanation:
Given,
5.26 + 1.93 we need to round to the nearest one.
First, take 5.26 and round to the nearest one.
5.26 = 5
Next, 1.93 we need to round to the nearest one.
1.93 = 2
Now add the estimated numbers 5 + 2 = 7
The sum is about 7.
Talk Math
Describe a real-world example when it might be appropriate to estimate rather than get the exact answer.
Answer:
Let us take a real-world example.
When we are shopping in the store and trying to stay the expenses within the budget. We will estimate the cost of any item we put in the cart before buying and we mentally calculate the bill in our head.
Guided Practice
Round each decimal to the nearest one. Then add or subtract.
Question 1.
2.8 + 1.3
Round to the nearest one.
2.8 → _____________
1.3 → _____________
Add.
___________ + ____________ = ____________
So, 2.8 + 1.3 is about _____________.
Answer:
4, 4.1
Explanation:
Given,
2.8 + 1.3
Round to the nearest one.
2.8 → 3
1.3 → 1
Add.
3 + 1 = 4
So, 2.8 + 1.3 is about 4.1
Question 2.
5.98 – 1.03
Round to the nearest one.
5.98 → _____________
1.3 → _____________
Subtract.
___________ – _____________ = _____________
So, 5.98 – 1.03 is about ____________.
Answer:
5, 4.95
Explanation:
Given,
5.98 – 1.03
Round to the nearest one.
5.98 → 6
1.3 → 2
Subtract.
6 – 2 = 4
So, 5.98 – 1.03 is about 4.95.
Independent Practice
Round each decimal to the nearest one. Then add or subtract.
Question 3.
10.08 + 5.6 = _____________
Answer:
16
Explanation:
Given,
10.08 + 5.6
10 + 6 = 16
Question 4.
10.4 + 32.8 = ______________
Answer:
43
Explanation:
Given,
10.4 + 32.8
Now add by rounding off the numbers
10 + 33 = 43
Question 5.
$42.01 – $5.92 = _____________
Answer:
36
Explanation:
Given,
$42.01 – $5.92
Now round off the values
42 – 6 = 36
Question 6.
75.2 + 82.3 = _____________
Answer:
87
Explanation:
Given,
75.2 + 82.3
Now round off the values
75 + 82 = 87.
Question 7.
Answer:
5
Explanation:
Question 8.
Answer:
5
Explanation:
Question 9.
Answer:
5
Explanation:
Round each decimal to the nearest ten. Then add or subtract.
Question 10.
23.78 + 10.45 = ___________
Answer:
34.23
Explanation:
Question 11.
83.69 – 55.41 = _____________
Answer:
28
Explanation:
Question 12.
Answer:
16
Explanation:
Question 13.
Answer:
39
Explanation:
Question 14.
Answer:
13
Explanation:
Problem Solving
Solve Exercises 15-17 by rounding to the nearest one.
Question 15.
The weights of Marisa and Toni’s televisions are shown in the table. About how much more does Marisa’s television weigh than Toni’s?
Answer:
Marisa’s television weighs 9 lb more than Toni’s.
Explanation:
Given,
Weight of Marisa’s television = 52.7 lb
Weight of Toni’s television = 43.9 lb
Now round the values to the nearest one
53 – 44 = 9 lb more than Toni’s.
Question 16.
Mathematical PRACTICE Model Math Sophia has $20. She buys a hair band for $3.99, gum for $1.29, and a brush for $6.75 Not including tax, estimate how much change she should receive. Show your work.
Answer:
$7.97 in change.
Explanation:
First, we would add $3.99, $1.29, and $6.75 to see the total amount she spent.
3.99 + 1.29 + 6.75 = $12.03
She spent a total of $12.03.
Now, subtract this amount from $20.
20 – 12.03 = 7.97
She receives $7.97 in change.
Question 17.
Malcolm buys a taco for $1.79 and milk for $1.29. About how much money does he spend? Show your work.
Answer:
$3.08.
Explanation:
Given,
Malcolm buys a taco for $1.79 and milk for $1.29.
Now add both of them to know how much they spent = 1.79 + 1.29 = $3.08
He spent $3.08 money to buy a taco.
HOT Problems
Question 18.
Mathematical PRACTICE Find the Error Kim wants to estimate 5.494 + 1.108 by first rounding to the nearest hundredth. Find her mistake and correct it.
Answer:
The error is 5.50. It should be 5.49.
Explanation:
Given,
The Error Kim wants to estimate 5.494 + 1.108
Question 19.
Building on the Essential Question When is estimating an effective tool?
Answer:
Without estimation tool we are not able to determine if their answer is within a reasonable range.
McGraw Hill My Math Grade 5 Chapter 5 Lesson 2 My Homework Answer Key
Practice
Round each decimal to the nearest one. Then add or subtract.
Question 1.
Answer:
2
Explanation:
Question 2.
Answer:
44
Explanation:
Question 3.
Answer:
30
Explanation:
Question 4.
3.872 + 2.409 = ____________
Answer:
6
Explanation:
Question 5.
9.086 – 2.419 = ___________
Answer:
7
Explanation:
Problem Solving
Solve Exercises 6-9 by rounding to the nearest one.
Question 6.
The table shows the average speeds of two airplanes in miles per hour. About how much faster is the Foxbat than the Hawkeye? Show your work.
Answer:
1488 mph.
Explanation:
Given,
speed of Hawkeye = 375.52 mph
The speed that is rounded to the nearest one is 376
Speed of Foxbat = 1864.29 mph
The speed that is rounded to the nearest one is 1864 mph
The difference between thme gives us about how much faster is the Foxbat than the Hawkeye.
1864 – 376 = 1488 mph
Question 7.
Aluminum and tin are both metals. The standard atomic weight for aluminum is 26.98. The standard atomic weight for tin is 118.71. Estimate the difference between the standard atomic weights of these two metals. Show your work.
Answer:
119 -27 = 92
Explanation:
Given,
The standard atomic weight for aluminum is = 26.98
The estimated weight = 27
The standard atomic weight for tin is = 118.71
The estimated weight = 119
The difference between the standard atomic weights of these two metals gives us the answer
119 – 27 = 92
Question 8.
Lorena and her cousin are fishing at the lake. They caught two largemouth bass. One fish weighs 71.27 ounces and the other fish weighs 38.86 ounces. Estimate the total weight of the two fish. Show your work.
Answer:
71 + 39 = 110 ounces.
Explanation:
Given,
One fish weighs = 71.27 ounces
The estimated One fish weighs = 71 ounces
The other fish weighs 38.86 ounces
The estimated other fish weighs 38.86 ounces = 39 ounces
Now add both of the fishes weights to find out the total weight of the two fish
71 + 39 = 110 ounces.
Question 9.
Mathematical PRACTICE Model Math The table shows the lengths of four trails at a horseback riding camp. Estimate the total length of all the trails. Show your work.
Answer:
3 + 2 + 4 + 3 = 12 miles.
Explanation:
Given,
The length of trail A = 2.6
The estimated length of trail A= 3
The length of trail B = 1.8
The estimated length of trail B = 2
The length of trail C = 4.2
The estimated length of trail C = 4
The length of trail D = 3.3
The estimated length of trail D = 3
The total estimated length of the trail = 3 + 2 + 4 + 3 = 12 miles.
Test Practice
Question 10.
Mr. Dixon bought a whiteboard that was on sale for $1,989.99. The regular price was $2,499.89. Which is the best estimate of the amount of money Mr. Dixon saved by buying the whiteboard on sale?
(A) $500
(B) $1,000
(C) $3,000
(D) $4,000
Answer:
$500
Explanation:
Given,
Mr. Dixon bought a whiteboard that was on sale for $1,989.99.
The regular price = $2,499.89.
Round off to the nearest tenths.
Then the price will be $2000 and $2500
The difference between them gives us the best estimate of the amount of money Mr. Dixon saved by buying the whiteboard on sale.
$2500 – $2000 = $500